A278708 - OEIS

%I #47 Mar 31 2026 18:39:56

%S 154,144,298,442,740,1182,1922,3104,5026,8130,13156,21286,34442,55728,

%T 90170,145898,236068,381966,618034,1000000,1618034,2618034,4236068,

%U 6854102,11090170,17944272,29034442,46978714,76013156,122991870,199005026,321996896,521001922

%N Fibonacci sequence starting 154, 144.

%C The number 1000000 is in this sequence. There is a famous problem that says that somebody deposited money into a bank 20 times, and each deposit was the sum of the previous two deposits. The final deposit was $1000000. What were the first two deposits? The answer is $154 and $144, leading to this sequence.

%H Michael De Vlieger, <a href="/A278708/b278708.txt">Table of n, a(n) for n = 1..4776</a>

%H Perplexus Dot Info contributor Ady Tzidon, <a href="https://web.archive.org/web/20170313183546/http://perplexus.info/show.php?pid=10222">Twenty deposits</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).

%F From _Elmo R. Oliveira_, Mar 31 2026: (Start)

%F G.f.: -2*(82*x-5)/(x^2+x-1).

%F a(n) = a(n-1) + a(n-2) for n > 2.

%F a(n) = 154*Fibonacci(n) - 10*Fibonacci(n-1). (End)

%p a:= n-> (<<0|1>, <1|1>>^n.<<-10, 154>>)[1, 1]:

%p seq(a(n), n=1..33);  # _Alois P. Heinz_, Mar 31 2026

%t LinearRecurrence[{1, 1}, {154, 144}, 33] (* _Michael De Vlieger_, Oct 03 2023 *)

%Y Cf. A000045.

%K nonn,easy

%O 1,1

%A _Bobby Jacobs_, Jan 11 2017

%E More terms from _Rémy Sigrist_, Oct 03 2023